Non-parametric estimation for the difference or ratio of median failure times for paired observations.

We propose a non-parametric method to calculate a confidence interval for the difference or ratio of two median failure times for paired observations with censoring. The new method is simple to calculate, does not involve non-parametric density estimates, and is valid asymptotically even when the two underlying distribution functions differ in shape. The method also allows missing observations. We report numerical studies to examine the performance of the new method for practical sample sizes.